111. Unknot (mathematics), noun. An ordinary physical knot isn’t equivalent to a mathematical knot, although the two bear some resemblance. One informal working definition of a mathematical knot might be that it is a closed loop (one with no loose ends) that exists in three-dimensional space.

Here are some knots.

The unknot is the simplest of all possible mathematical knotsāit consists of a closed loop with no crossings in it. It looks like a circle. One of the fundamental questions in knot theory is the following: Given a knot, is it the unknot? On the face of it this is a trivial question, but in fact there are many ways in which the same knot can be stretched, twisted, or tangled until it looks like another. The simple unknot can often be found hiding behind the deformations of a knot that looks more complicated.

From Old English un, a negating prefix, + cnotta, “intertwining.”

You’ve finished what you started. Some paths, though snarled, lead clear through to the perfect end.

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